Key Features of Linear Functions

Front

What is the slope of a linear function?

Back

The slope of a linear function is a measure of its steepness, calculated as the change in y divided by the change in x (rise over run).

Front

How do you find the y-intercept of a linear function?

Back

The y-intercept is found by setting x to 0 in the equation of the function and solving for y.

Front

What does a positive slope indicate about a linear function?

Back

A positive slope indicates that as x increases, y also increases, resulting in an upward slant of the graph.

Front

What does a negative slope indicate about a linear function?

Back

A negative slope indicates that as x increases, y decreases, resulting in a downward slant of the graph.

Front

What does a slope of zero mean for a linear function?

Back

A slope of zero means the function is a horizontal line, indicating that y remains constant regardless of x.

Front

What does an undefined slope indicate?

Back

An undefined slope indicates a vertical line, where x remains constant and y can take any value.

Front

How do you determine the slope from two points (x1, y1) and (x2, y2)?

Back

The slope (m) is calculated using the formula m = (y2 - y1) / (x2 - x1).

Front

What is the standard form of a linear equation?

Back

The standard form of a linear equation is Ax + By = C, where A, B, and C are integers.

Front

What is the slope-intercept form of a linear equation?

Back

The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

Front

How can you convert from standard form to slope-intercept form?

Back

To convert, solve for y in the equation Ax + By = C to get y = mx + b.